What is Middle School Math?
How would you determine a budget, estimate costs or quantities for a construction project, calculate an interest rate for a car payment or home, or figure out how much mulch you'll need for your garden? These are practical everyday questions that math helps us understand. Math, in my own definition, helps us calculate, estimate, or find missing quantities, analyze, chart and represent data and data trends from various sources, relate or explain a relationship using quantities, or characteristics of things, and prove and show how something works, or explain a relationship . Math also can help us determine critical information about natural phenomenon, such as light, gravity or sound, and relates to NUMEROUS other fields - Engineering, physics, chemistry, geology, medicine, art, music, etc.... the list goes on. Essentially math ties into our everyday life.
Defining mathematics is a big undertaking, so I'd like to focus on the mathematics skills that you learn in middle school. 7th and 8th grade mathematics is a very exciting time for students! In a nutshell, in middle school mathematics, we are preparing for Algebra and Geometry and other high school math subjects, such as Statistics and Probability. Therefore its important that students learn and build the foundational math skill sets that will help them transition smoothly into these subjects. Below, I’ve outlined the mathematical concepts students learn in middle school, and how they relate to each grade level based on the CA Common Core State Standards.
One overall theme of middle school math according to the Common Core Standards is the readiness for algebra. According to the Council of Chief State School Officers (CCSSO) website videos, the emphasis of these particular concepts is so that students can “rehearse” for algebra and not be afraid of it when they reach high school. These middle school math concepts or domains, as the mathematics team from CCSSO put it, should “…be a ramp for students to enter algebra... not a cliff”. The first big concept for algebraic readiness is ratios and proportions. Ratios and proportions are utilized also in geometry, and statistics and probability. In 6th grade, students start thinking about percentages and expressions of ratios in terms of fractions and decimals, then they move on to more real world applications of these ratios and proportions in 7th grade, and start to deal with unit rates, and then in 8th grade, these concepts are united into the introduction of functions, where students are solving for unknowns and relating the slopes of linear equations to ratios and proportions. According to the Council of Chief State School Officers (CCSSO) videos, the goal for middle school math students is to become familiar with skills such as calculating the rainfall per area, the cost per unit rate, and this focus on ratios and proportions is essential for college and life beyond the classroom. Other concepts, such as the number system and expressions and equations tie very nicely into the algebraic readiness theme. For instance, students in the 6th grade take what they know about the number line and fractions, and build on their knowledge of multiplication and division, and start learning how to solve basic one variable unknown equations and inequalities by applying multiplication and division properties and learning how to manipulate equations. In 7th grade, this understanding deepens when students start to solve more complicated equations and inequalities with fractions and start to incorporate operations with positive and negative numbers and absolute values, which also builds on their number system knowledge. Finally in 8th grade math, students start applying exponential properties to this knowledge of solving for unknowns, and their understanding of the number system builds even more, by learning irrational numbers such as e, pi, and root 2, and how to work with these irrational numbers into algebraic operations. Overall, students deepen and refine their understanding of these foundational concepts of ratios, proportions, number system, and expressions and equations every year in middle school, to prepare them for algebra courses in high school.
Another big theme in the Common Core Standards is geometry and statistics and probability. These subjects are typical subjects for 9th and 10th grade, and statistics and probability may be incorporated into another class, such as Trigonometry, or presented as a standalone class. The concepts of geometry are introduced in 6th grade, when students start relating real world experiences to problems that ask them to identify and solve for surface area, total area, and volume. In 7th grade, students practice the construction of geometric figures and learn about angles, which deepen their first experience of geometric properties in 6th grade. In 8th grade, students learn about the Pythagorean Theorem, congruence and similarity and are encouraged to explore congruence and similarity using real world models (such as geoboards, class projects, multi-media programs, etc.).
Pertaining to statistics and probability, students in 6th grade are introduced to basic statistical terminology and the concept of data distributions, by looking at the many ways data can be represented. They learn how to identify classic data models for large and small data distributions, such as a histogram, or a box and whisker plot. In 7th grade, students start inferring information from these models and start to investigate the way data is collected and used to create these models. In other words, they learn more about the methods behind the distributions they first learned to identify. In addition, they are introduced to the concept of chance and likelihood of occurrence (chance models), and must investigate which probability models are appropriate for scenarios. By 8th grade, the concept of patterns of data that is bivariate, or relating to 2 quantitative variables, such as growth and time, or decay and time, is presented and practiced. This strong base knowledge of geometry and statistics and probability will provide students with a smooth transition into the high school and college math classes, where the application of these topics will be applied and explored in more depth.
References
Common Core State Standards Initiative Website. http://www.corestandards.org/Math/ and
California Department of Education. CA Common Core State Standards. http://www.cde.ca.gov/be/st/ss/documents/ccssmathstandardaug2013.pdf
Council of Chief School State Officers. Common Core Implementation Video Series. http://www.ccsso.org/resources/digital_resources/common_core_implementation_video_series.html
Common Core State Standards Initiative Website. http://www.corestandards.org/Math/ and
California Department of Education. CA Common Core State Standards. http://www.cde.ca.gov/be/st/ss/documents/ccssmathstandardaug2013.pdf
Council of Chief School State Officers. Common Core Implementation Video Series. http://www.ccsso.org/resources/digital_resources/common_core_implementation_video_series.html
Math is fun! Watch these videos to see other 7th and 8th graders in action during class time!
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